## Personal Knowledge and Interpretation of Statistical Data

This post is a response to some of the sentiments expressed in response to these articles:

http://news.ycombinator.com/item?id=2607751

http://news.ycombinator.com/item?id=1978295

To summarize, a lot of people are highly critical of the decisions of individuals to take a 1/10 chance of death in summiting Mt. Everest.

This type of criticism causes me deep anguish. On the one hand, given that the people know nothing about the individuals they are criticizing, they are technically correct. On the other hand, a refutation from an individual of the form “Fuck you! I’m gonna climb that shit! I’m strong as hell!” is very difficult to effectively contradict:

One deep problem when applying a statistic of this type to an individual is that a statistic is a statement about the properties of an individual given no information other than intent. Straightforward statistical analysis is egalitarian – it relies on the assumption that people are fundamentally similar. What gets complicated is that, from the perspective of an outsider who has no information, they are, but from the perspective of the individual who has lots of information, they aren’t necessarily.

Suppose you’re confronting a person who’s going to climb Mt. Everest –

Naysayer: “But you have kids! You have a 1/10 chance of dying!”

Climber: “No, actually, the average person who attempts to summit Everest has a 1/10 chance of dying – but I’ve been climbing for 20 years and have done much harder climbs…so my probability is lower”

The Naysayer is now in a very complicated position. He has no knowledge about how the conditional probability of death in attempting to summit Everest varies with experience – and what’s more, we expect that not everyone who climbs Everest has 20 years of experience, that experience is probably useful, and so probably this person has a higher chance of living – but how much higher?

In formal terms, the problem is that all we know is P(Death), we don’t know P(Death | X) for ANY X. So how do we respond when someone says “oh, but X!” (for any X!)

E.g. “oh, but I’m SUPER strong – and I climb 5.13’s in the gym!”

E.g. “oh, but I’ve summited Kilimanjaro!”

E.g. “oh, but I have very good circulation!”

To refute these claims would require a lot of effort on your part – you’d have to do a thorough analysis of the influence of these conditions on probability of success – as well as a quantitative analysis of the subject.

More purely, as soon as you know *anything about the person *you are forced to evaluate the conditional probability given what you know – but you generally don’t know how to do that.

The real *crux* of the issue is that you might have beliefs about the action outside of a purely statistics-based expected value calculation. E.g. maybe you “really believe” that the guy can climb the mountain! How do you compare a conditional probability that you can’t evaluate with a qualitative claim? God only knows!

—–

This is to say that statistical analysis is basically useless with respect to its application to a known individual.

It *is *useful when it comes to decisions regarding a population (e.g. policy decisions) as long as you don’t have any information about how properties of the population are distributed.

It *is *useful if you think you’re just like anyone else, or if you know nothing about the individual.

—–

This is to stay – stop crossing the bounds, motherfucker!

leave a comment